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In the same stockpot, add the oil. Combine the lobster shells with the carrot, celery, onion, garlic, rosemary, thyme, peppercorns, water, and ketchup. Bring the mixture to a simmer and let reduce for 2 hours. Strain and transfer 6 cups/1.5 L of the remaining stock into a smaller saucepan, reducing on medium heat for another 20 minutes or until approximately 1/3 of the stock is left. Remove from the heat and set aside.
Bring a pot of salted water to a boil and add the fettuccine. Cook 1 minute less than instructed. Strain and set aside.
Heat 1 tablespoon olive oil in a pan on medium heat and add the shallot. Saute 1 minute, then add the garlic and continue cooking for another 2 minutes. Add stock. Add the pasta, reserved lobster meat, peas, and chives, and 2 tablespoons butter and mix well. Salt, and pepper, to taste.
Cook's Note: Any leftover lobster stock can be kept in the freezer for up to 3 months.